How do u define this <u|A|u>? where A is a selfadjoint linear operator. I have one book that defines is as ||A|u>||^2=<u|A|u> (equation 2.6 http://www.theory.caltech.edu/people/preskill/ph229/notes/chap2.ps) and since ||A|u>||^2 is the lenght of the vector A|u> squared that is equal to (<u|A)(A|u>). I have another book (j.j sakurai) that defines it as (<u|)(A|u>)=(<u|A)(|u>)=<u|A|u> but this is the projection of A|u> on |u>. It seems to me that the two definitions arent equal !? Any ideas?